Given an edge-weighted graph G, the minimum maximal matching problem asks to find a minimum weight maximal matching. The problem is known to be NP-hard even if the graph is planar and unweighted. In this paper, we consider the problem in planar graphs. First, we prove a strong inapproximability for the problem in weighted planar graphs. Second, in contrast with the first result, we show that a polynomial time approximation scheme (PTAS) for the problem in unweighted planar graphs can be obtained by a divide-and-conquer method based on the planar separator theorem. For a given ε > 0, our scheme delivers in time a solution with size at most (1 + ε) times the optimal value, where n is the number of vertices in G and α is a constant number.

We newly propose a stable algorithm for blind source separation (BSS) combining multistage ICA (MSICA) and linear prediction. The MSICA is the method previously proposed by the authors, in which frequency-domain ICA (FDICA) for a rough separation is followed by time-domain ICA (TDICA) to remove residual crosstalk. For temporally correlated signals, we must use TDICA with a nonholonomic constraint to avoid the decorrelation effect from the holonomic constraint. However, the stability cannot be guaranteed in the nonholonomic case. To solve the problem, the linear predictors estimated from the roughly separated signals by FDICA are inserted before the holonomic TDICA as a prewhitening processing, and the dewhitening is performed after TDICA. The stability of the proposed algorithm can be guaranteed by the holonomic constraint, and the pre/dewhitening processing prevents the decorrelation. The experiments in a reverberant room reveal that the algorithm results in higher stability and separation performance.

An adaptive blind signal separation filter is proposed using a risk-sensitive criterion framework. This criterion adopts an exponential type function. Hence, the proposed criterion varies the consideration weight of an adaptation quantity depending on errors in the estimates: the adaptation is accelerated when the estimation error is large, and unnecessary acceleration of the adaptation does not occur close to convergence. In addition, since the algorithm derivation process relates to an H filtering, the derived algorithm has robustness to perturbations or estimation errors. Hence, this method converges faster than conventional least squares methods. Such effectiveness of the new algorithm is demonstrated by simulation.

Many feature tracking algorithms have been proposed for motion segmentation, but the resulting trajectories are not necessarily correct. In this paper, we propose a technique for removing outliers based on the knowledge that correct trajectories are constrained to be in a subspace of their domain. We first fit an appropriate subspace to the detected trajectories using RANSAC and then remove outliers by considering the error behavior of actual video tracking. Using real video sequences, we demonstrate that our method can be applied if multiple motions exist in the scene. We also confirm that the separation accuracy is indeed improved by our method.

We propose a new algorithm for blind source separation (BSS), in which frequency-domain independent component analysis (FDICA) and time-domain ICA (TDICA) are combined to achieve a superior source-separation performance under reverberant conditions. Generally speaking, conventional TDICA fails to separate source signals under heavily reverberant conditions because of the low convergence in the iterative learning of the inverse of the mixing system. On the other hand, the separation performance of conventional FDICA also degrades significantly because the independence assumption of narrow-band signals collapses when the number of subbands increases. In the proposed method, the separated signals of FDICA are regarded as the input signals for TDICA, and we can remove the residual crosstalk components of FDICA by using TDICA. The experimental results obtained under the reverberant condition reveal that the separation performance of the proposed method is superior to those of TDICA- and FDICA-based BSS methods.

This paper presents novel techniques for blind separation and blind extraction of instantaneously mixed binary sources, which are suitable for the case with less sensors than sources. First, a solvability analysis is presented for a general case. Necessary and sufficient conditions for recoverability of all or some part of sources are derived. A new deterministic blind separation algorithm is then proposed to estimate the mixing matrix and separate all sources efficiently in the noise-free or low noise level case. Next, using the Maximum Likelihood (ML) approach for robust estimation of centers of clusters, we have extended the algorithm for high additive noise case. Moreover, a new sequential blind extraction algorithm has been developed, which enables us not only to extract the potentially separable sources but also estimate their number. The sources can be extracted in a specific order according to their dominance (strength) in the mixtures. At last, simulation results are presented to illustrate the validity and high performance of the algorithms.

We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low-convergence problem through optimization in ICA. The proposed method consists of the following two parts: frequency-domain ICA with direction-of-arrival (DOA) estimation, and null beamforming based on the estimated DOA. The alternation of learning between ICA and beamforming can realize fast- and high-convergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICA-based BSS method.

In many applications of Independent Component Analysis (ICA) and Blind Source Separation (BSS) estimated sources signals and the mixing or separating matrices have some special structure or some constraints are imposed for the matrices such as symmetries, orthogonality, non-negativity, sparseness and specified invariant norm of the separating matrix. In this paper we present several algorithms and overview some known transformations which allows us to preserve several important constraints.

Blind separation of sources from their linear mixtures is a well understood problem. However, if the mixtures are nonlinear, this problem becomes generally very difficult. This is because both the nonlinear mapping and the underlying sources must be learned from the data in a blind manner, and the problem is highly ill-posed without a suitable regularization. In our approach, multilayer perceptrons are used as nonlinear generative models for the data, and variational Bayesian (ensemble) learning is applied for finding the sources. The variational Bayesian technique automatically provides a reasonable regularization of the nonlinear blind separation problem. In this paper, we first consider a static nonlinear mixing model, with a successful application to real-world speech data compression. Then we discuss extraction of sources from nonlinear dynamic processes, and detection of abrupt changes in the process dynamics. In a difficult test problem with chaotic data, our approach clearly outperforms currently available nonlinear prediction and change detection techniques. The proposed methods are computationally demanding, but they can be applied to blind nonlinear problems of higher dimensions than other existing approaches.

In this paper we consider blind source separation (BSS) problem of signals which are spatially uncorrelated of order four, but temporally correlated of order four (for instance speech or biomedical signals). For such type of signals we propose a new sufficient condition for separation using fourth order statistics, stating that the separation is possible, if the source signals have distinct normalized cumulant functions (depending on time delay). Using this condition we show that the BSS problem can be converted to a symmetric eigenvalue problem of a generalized cumulant matrix Z(4)(b) depending on L-dimensional parameter b, if this matrix has distinct eigenvalues. We prove that the set of parameters b which produce Z(4)(b) with distinct eigenvalues form an open subset of RL, whose complement has a measure zero. We propose a new separating algorithm which uses Jacobi's method for joint diagonalization of cumulant matrices depending on time delay. We empasize the following two features of this algorithm: 1) The optimal number of matrices for joint diago- nalization is 100-150 (established experimentally), which for large dimensional problems is much smaller than those of JADE; 2) It works well even if the signals from the above class are, additionally, white (of order two) with zero kurtosis (as shown by an example).

A new blind identification method of transfer functions between variables in feedback systems is introduced for single sweep type of MEG data. The method is based on the viewpoint of stochastic/statistical inverse problems. The required conditions of the model are stationary and linear Gaussian processes. Raw MEG data of the brain activities are heavily contaminated with several noises and artifacts. The elimination of them is a crucial problem especially for the method. Usually, these noises and artifacts are removed by notch and high-pass filters which are preset automatically. In the present paper, we will try two types of more careful preprocessing procedures for the identification method to obtain impulse functions. One is a careful notch filtering and the other is a blind source separation method based on temporal structure. As results, identifiably of transfer functions and their impulse responses are improved in both cases. Transfer functions and impulse responses identified between MEG sensors are obtained by using the method in Appendix A, when eyes are closed with rest state. Some advantages of the blind source separation method are discussed.

The problem of separating blindly independent sources from a convolutive mixture cannot be addressed in its widest generality without resorting to statistics of order higher than two. The core of the problem is in fact to identify the paraunitary part of the mixture, which is addressed in this paper. With this goal, a family of statistical contrast is first defined. Then it is shown that the problem reduces to a Partial Approximate Joint Diagonalization (PAJOD) of several cumulant matrices. Then, a numerical algorithm is devised, which works block-wise, and sweeps all the output pairs. Computer simulations show the good behavior of the algorithm in terms of Symbol Error Rates, even on very short data blocks.

As pseudorandom number generators for Monte Carlo simulations, inversive linear congruential generators (ICG) have some advantages compared with traditional linear congruential generators. It has been shown that a sequence generated by an ICG has a low discrepancy even if the length of the sequence is far shorter than its period. In this paper, we formulate fractional linear congruential generators (FCG), a generalized concept of the inversive linear congruential generators. It is shown that the sequence generated by an FCG is a geometrical shift of a sequence from an ICG and satisfies the same upper bounds of discrepancy. As an application of the general formulation, we show that under certain condition, "Leap-Frog technique," a way of splitting a random number sequence to parallel sequences, can be applied to the ICG or FCG with no extra cost on discrepancy.

This paper addresses a maximum likelihood method for source separation in the case of overdetermined mixtures corrupted by additive white Gaussian noise. We consider an approximate likelihood which is based on the Laplace approximation and develop a natural gradient adaptation algorithm to find a local maximum of the corresponding approximate likelihood. We present a detailed mathematical derivation of the algorithm using the Lie group invariance. Useful behavior of the algorithm is verified by numerical experiments.

This letter presents parallel algorithms for matrix multiplication and the fast Fourier transform (FFT) that are significant problems arising in engineering and scientific applications. The proposed algorithms are designed on a 3-dimensional processor array with separable buses (PASb). We show that a PASb consisting of N N h processors can compute matrix multiplication of size N N and the FFT of size N in O(N/h+log N) time, respectively. In order to examine ease of hardware implementation, we also evaluate the VLSI complexity of the algorithms. A result obtained achieves an optimal bound on area-time complexity when h=O(N/log N).

This paper presents a flexible learning algorithm for the binary neural network that can realize a desired Boolean function. The algorithm determines hidden layer parameters using a genetic algorithm. It can reduce the number of hidden neurons and can suppress parameters dispersion. These advantages are verified by basic numerical experiments.

This paper proposes a design method of 2-D variable IIR digital filters with high frequency tuning accuracy. In the proposed method, a parallel complex allpass structure is used as the prototype structure of the 2-D variable digital filters in order to obtain low sensitivity characteristic. Because the proposed 2-D variable digital filter is composed of first-order complex allpass sections connected in parallel, the proposed variable digital filter possesses several advantages such as low sensitivity characteristic in the passband, simple stability monitoring and high parallelism. In order to improve the frequency tuning accuracy of the proposed variable digital filter, each first-order complex allpass section is substituted by a new first-order complex allpass section with low sensitivity characteristic. Moreover, the coefficient sensitivity analysis of a 2-D parallel complex allpass structure is presented. Numerical examples show that the proposed 2-D variable IIR digital filter has high tuning accuracy under the finite coefficient wordlength.

A design method is proposed that yields the optimum remote pre-amplifier (RPRA) parameters considering cable repair, the results of include increased cable loss and insertion position uncertainty. The optimum RPRA location is given by the intersection point of optical SNR (OSNR) vs. RPRA location curves in two cases; the total cable repair loss is assumed to be inserted at the transmitter end and at the receiver end. This RPRA parameter gives the maximum OSNR in the worst loss insertion case by cable repair.

We have developed optical encoding devices for processing femtosecond pulses. These devices are based on spectral separation devices and light modulators with fiber gratings. Experiments were made to encode a light pulse in the spectral domain. These experiments utilize the characteristics that a femtosecond light pulse has a very broad spectrum. An input femtosecond light pulse is decomposed into a series of wavelength components. Each wavelength component with narrow spectra <1 nm width is successfully extracted into a single mode fiber. Light modulators corresponding to wavelength components are assigned to the 1st bit, the 2nd bit, the 3rd bit, , the nth bit, respectively. All of the encoded wavelength components are again recombined into a single time-varying signal and transmitted through an optical fiber. Decoding at receiving site is made by the reverse operation. Encoding and decoding for 2-bit and 4-bit signals were demonstrated for 200 fs input light pulse with about 40 nm spectral width.

We examine diagnosis of processor array systems formed as two-dimensional grids, with boundaries, and either four or eight neighbors for each interior processor. We employ a parallel test schedule. Neighboring processors test each other and report the results. Our diagnostic objective is to find a fault-free processor or set of processors. The system may then be sequentially diagnosed by repairing those processors tested faulty according to the identified fault-free set. We establish an upper bound on the maximum number of faults that can be sustained without invalidating the test results under worst case conditions. We give test schedules and diagnostic algorithms that meet the upper bound as far as the highest order term. We compare these near optimal diagnostic algorithms to alternative algorithms--both new and already in the literature.